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Geometry 2 (Discrete Group Theory) Lab
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The lab studies random walks on discrete groups.
AboutAbout the lab
Exploring random walks wandering over groups
Prof. Tanaka's lab studies discrete group theory and discrete probability theory in the field of geometry.
Its main themes are random walks on groups and Markov chains.
The lab investigates how random walks on hyperbolic groups and affine Weyl groups respond to small fluctuations.
Key terms
- Random walk
- Movement in which the destination is chosen randomly at each step
- Markov chain
- A process in which the next state is determined probabilistically by the current state alone
- Hyperbolic group
- A group that, viewed from afar, spreads out like the hyperbolic plane
ResearchResearch themes
The lab studies discrete group theory, discrete probability theory, random walks, and Markov chains.
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MembersFaculty
- Associate ProfessorRyokichi Tanaka
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Loop erased random walk in 2D” Cosmia Nebula / CC BY-SA 4.0 (cropped)
- Noise sensitivity on groups: “A4 Cayley graph” נוצר על ידי משתמש:עוזי ו. / CC BY-SA 3.0 (cropped)
- Related lab (Algebra 1 (Number Theory) Lab (Ito)): “EllipticGroup” Thomas Cooper / Public domain (cropped)
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